1. Field of the Invention
This invention relates to a leapfrog filter, and more particularly it pertains to such a filter which is so designed that adjustment of the quality factor Q and center frequency f.sub.0 of the filter characteristics is facilitated.
2. Description of the Prior Art
Referring to FIG. 1, description will first be made of an example of conventional active filter, which is constructed in the form of biquad circuit constituting a low-pass filter. The transfer function T(S) of a common low-pass filter is given as follows: ##EQU1## where .omega..sub.0 is angular frequency; s is complex variable; Q is loss factor of coil; and H is gain factor.
The relationship between input and output voltages V.sub.1 and V.sub.2 of the biquad circuit can be expressed in the form of transfer function T(S) as follows: ##EQU2##
Assuming that the factor of each term in Equation (1) and that in Equation (2) are equal to each other, the angular frequency .omega..sub.0 and quality factor Q are given as follows: EQU .omega..sub.0.sup.2 =1/R.sub.3 R.sub.4 C.sub.1 C.sub.2 ( 3) EQU Q=(R.sub.1.sup.2 C.sub.1 /R.sub.2 R.sub.4 C.sub.2).sup.1/2 ( 4)
As will be seen from Equations (3) and (4), it is required that circuit constants such as resistors R.sub.1 to R.sub.4 or capacitors C.sub.1 and C.sub.2 be made variable to make variable the center frequency f.sub.0 and quality factor Q. With biquad circuit, to make variable the center frequency f.sub.0 and quality factor Q, externally mounted components are used as the resistors R.sub.1 to R.sub.4 or capacitors C.sub.1 and C.sub.2, and the filter characteristic is adjusted by changing the circuit constants. With the conventional active filter such as biquad circuit, it has been the usual practice that a number of components such as operational amplifiers resistors, capacitors and so forth are hybrid-integrated on a hybrid substrate.
However, the conventional active filter such as shown in FIG. 1 is disadvantageous in that the manufacturing cost is high because a number of components are needed. Another disadvantage is such that when it is attempted to adjust the center frequency f.sub.0 and quality factor Q of the filter, it is required that such adjustment be effected with components having different circuit constants being mounted on a printed circuit board in accordance with the desired filter characteristic.